On the Minrank of Symmetric and Neighboring Side-information Index Coding Problems

Vaddi, MB and Rajan, BS (2019) On the Minrank of Symmetric and Neighboring Side-information Index Coding Problems. In: 2019 IEEE Information Theory Workshop, ITW 2019, 25-28, August 2019, Sweden.

PDF iee_inf_the_wor_2019.pdf - Published Version Restricted to Registered users only Download (174kB) | Request a copy

Abstract

The length of an optimal scalar linear index code of a single unicast index coding problem (SUICP) is equal to the minrank of its side-information graph. A single unicast index coding problem is called symmetric neighboring and consecutive (SNC) side-information problem if it has K messages and K receivers, the kth receiver Rk wanting the kth message xk and having the side-information D messages immediately after xk and U (D�U) messages immediately before xk. Maleki, Cadambe and Jafar obtained the capacity of this SUICP(SNC) and proposed (U+1)-dimensional optimal length vector linear index codes by using Vandermonde matrices. However, for a b-dimensional vector linear index code, the transmitter needs to wait for b realizations of each message and hence the latency introduced at the transmitter is proportional to b. For any given single unicast index coding problem with the side-information graph G, MAIS (G) is used to give a lowerbound on the broadcast rate of the ICP. In this paper, we analyse the properties of minrank of SUICP(SNC) side-information graph. We derive the MAIS (G) of side-information graph G of SUICP(SNC). For arbitrary K, D and U, we construct scalar linear index codes for SUICP(SNC) with length 1/4KU+1-1/4 D-UU+1. We obtain the minrank of SUICP(SNC) side-information graph and show that the length of the constructed scalar linear index codes is equal to minrank of SUICP(SNC) side-information graph for some combinations of K, D and U. © 2019 IEEE.

Item Type:	Conference Paper
Publication:	2019 IEEE Information Theory Workshop, ITW 2019
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	cited By 0; Conference of 2019 IEEE Information Theory Workshop, ITW 2019 ; Conference Date: 25 August 2019 Through 28 August 2019; Conference Code:157627
Keywords:	Graph theory; Optimal systems; Transmitters, Dimensional vectors; Graph G; Index coding; Lower bounds; Side information; Unicast; Vandermonde matrix, Codes (symbols)
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	17 Aug 2020 10:41
Last Modified:	17 Aug 2020 10:41
URI:	http://eprints.iisc.ac.in/id/eprint/64914

Actions (login required)

View Item